1. Field of the Invention
The present invention relates to a measurement (stitch) for making a plurality of partial measurements, and obtaining an overall shape by combining partial measurement results.
2. Description of the Related Art
A stitch technique was born to avoid cost required to manufacture a large reference optical element used to test an astronomical mirror. For a while since its birth, partial measurement regions did not have any overlapping region, and polynomial fitting was executed with reference to “global smoothness”. For this reason, high-resolution information of partial measurement data was lost. In recent years, partial measurement regions have an overlapping region, and combination is executed with reference to “self-consistency”. As a result, high-resolution information of partial measurement data can be held.
Respective partial measurements include individual set errors (position/orientation errors). The respective partial measurements include system errors (errors unique to a measurement apparatus) equivalent to all the partial measurements. The stitch technique is also required to correct these set errors and system errors. U.S. Pat. No. 6,956,657 discloses a method for simultaneously calculating the set errors and system errors.
Conventionally, since each partial measurement region in an interference measurement has a circular shape, the Zernike polynomials as a sequence of functions which are orthogonal on a circle were used to define the system errors. In this case, since system error correction on circular partial measurement regions was executed using data of non-circular data existence regions although there was no data outside the overall measurement region on lattices (locations of the partial measurement regions), the precision drops. For the same reason as above, coefficients of bases were different depending on bases of the Zernike polynomials used in system error definition.